fractions --- 有理數¶

原始碼：Lib/fractions.py

Thefractions module provides support for rational number arithmetic.

A Fraction instance can be constructed from a pair of rational numbers, froma single number, or from a string.

classfractions.Fraction(numerator=0,denominator=1)¶

classfractions.Fraction(number)

classfractions.Fraction(string)

The first version requires thatnumerator anddenominator are instancesofnumbers.Rational and returns a newFraction instancewith a value equal tonumerator/denominator.Ifdenominator is zero, it raises aZeroDivisionError.

The second version requires thatnumber is an instance ofnumbers.Rational or has theas_integer_ratio() method(this includesfloat anddecimal.Decimal).It returns aFraction instance with exactly the same value.Assumed, that theas_integer_ratio() method returns a pairof coprime integers and last one is positive.Note that due to theusual issues with binary point (see浮點數運算：問題與限制), theargument toFraction(1.1) is not exactly equal to 11/10, and soFraction(1.1) doesnot returnFraction(11,10) as one might expect.(But see the documentation for thelimit_denominator() method below.)

The last version of the constructor expects a string.The usual form for this instance is:

[sign]numerator['/'denominator]

where the optionalsign may be either '+' or '-' andnumerator anddenominator (if present) are strings ofdecimal digits (underscores may be used to delimit digits as withintegral literals in code). In addition, any string that represents a finitevalue and is accepted by thefloat constructor is alsoaccepted by theFraction constructor. In either form theinput string may also have leading and/or trailing whitespace.Here are some examples:

>>>fromfractionsimportFraction>>>Fraction(16,-10)Fraction(-8, 5)>>>Fraction(123)Fraction(123, 1)>>>Fraction()Fraction(0, 1)>>>Fraction('3/7')Fraction(3, 7)>>>Fraction(' -3/7 ')Fraction(-3, 7)>>>Fraction('1.414213\t\n')Fraction(1414213, 1000000)>>>Fraction('-.125')Fraction(-1, 8)>>>Fraction('7e-6')Fraction(7, 1000000)>>>Fraction(2.25)Fraction(9, 4)>>>Fraction(1.1)Fraction(2476979795053773, 2251799813685248)>>>fromdecimalimportDecimal>>>Fraction(Decimal('1.1'))Fraction(11, 10)

TheFraction class inherits from the abstract base classnumbers.Rational, and implements all of the methods andoperations from that class.Fraction instances arehashable,and should be treated as immutable. In addition,Fraction has the following properties and methods:

在 3.2 版的變更:Fraction 建構函式現在可接受float 和decimal.Decimal 實例。

在 3.9 版的變更:Themath.gcd() function is now used to normalize thenumeratoranddenominator.math.gcd() always returns anint type.Previously, the GCD type depended onnumerator anddenominator.

在 3.11 版的變更:Underscores are now permitted when creating aFraction instancefrom a string, followingPEP 515 rules.

在 3.11 版的變更:Fraction implements__int__ now to satisfytyping.SupportsInt instance checks.

在 3.12 版的變更:Space is allowed around the slash for string inputs:Fraction('2/3').

在 3.12 版的變更:Fraction instances now support float-style formatting, withpresentation types"e","E","f","F","g","G"and"%"".

在 3.13 版的變更:Formatting ofFraction instances without a presentation typenow supports fill, alignment, sign handling, minimum width and grouping.

在 3.14 版的變更:Fraction 建構函式現在可接受任何具有as_integer_ratio() 方法的物件。

numerator¶

Numerator of the Fraction in lowest term.

denominator¶

Denominator of the Fraction in lowest terms.Guaranteed to be positive.

as_integer_ratio()¶

Return a tuple of two integers, whose ratio is equalto the original Fraction. The ratio is in lowest termsand has a positive denominator.

在 3.8 版被加入.

is_integer()¶

ReturnTrue if the Fraction is an integer.

在 3.12 版被加入.

classmethodfrom_float(f)¶

Alternative constructor which only accepts instances offloat ornumbers.Integral. Beware thatFraction.from_float(0.3) is not the same value asFraction(3,10).

備註

From Python 3.2 onwards, you can also construct aFraction instance directly from afloat.

classmethodfrom_decimal(dec)¶

Alternative constructor which only accepts instances ofdecimal.Decimal ornumbers.Integral.

備註

From Python 3.2 onwards, you can also construct aFraction instance directly from adecimal.Decimalinstance.

classmethodfrom_number(number)¶

Alternative constructor which only accepts instances ofnumbers.Integral,numbers.Rational,float ordecimal.Decimal, and objects withtheas_integer_ratio() method, but not strings.

在 3.14 版被加入.

limit_denominator(max_denominator=1000000)¶

Finds and returns the closestFraction toself that hasdenominator at most max_denominator. This method is useful for findingrational approximations to a given floating-point number:

>>>fromfractionsimportFraction>>>Fraction('3.1415926535897932').limit_denominator(1000)Fraction(355, 113)

or for recovering a rational number that's represented as a float:

>>>frommathimportpi,cos>>>Fraction(cos(pi/3))Fraction(4503599627370497, 9007199254740992)>>>Fraction(cos(pi/3)).limit_denominator()Fraction(1, 2)>>>Fraction(1.1).limit_denominator()Fraction(11, 10)

__floor__()¶

Returns the greatestint<=self. This method canalso be accessed through themath.floor() function:

>>>frommathimportfloor>>>floor(Fraction(355,113))3

__ceil__()¶

Returns the leastint>=self. This method canalso be accessed through themath.ceil() function.

__round__()¶

__round__(ndigits)

The first version returns the nearestint toself,rounding half to even. The second version roundsself to thenearest multiple ofFraction(1,10**ndigits) (logically, ifndigits is negative), again rounding half toward even. Thismethod can also be accessed through theround() function.

__format__(format_spec,/)¶

Provides support for formatting ofFraction instances via thestr.format() method, theformat() built-in function, orFormatted string literals.

If theformat_spec format specification string does not end with oneof the presentation types'e','E','f','F','g','G' or'%' then formatting follows the general rules for fill,alignment, sign handling, minimum width, and grouping as described in theformat specification mini-language. The "alternateform" flag'#' is supported: if present, it forces the output stringto always include an explicit denominator, even when the value beingformatted is an exact integer. The zero-fill flag'0' is notsupported.

If theformat_spec format specification string ends with one ofthe presentation types'e','E','f','F','g','G' or'%' then formatting follows the rules outlined for thefloat type in the格式規格 (Format Specification) 迷你語言 section.

Here are some examples:

>>>fromfractionsimportFraction>>>format(Fraction(103993,33102),'_')'103_993/33_102'>>>format(Fraction(1,7),'.^+10')'...+1/7...'>>>format(Fraction(3,1),'')'3'>>>format(Fraction(3,1),'#')'3/1'>>>format(Fraction(1,7),'.40g')'0.1428571428571428571428571428571428571429'>>>format(Fraction('1234567.855'),'_.2f')'1_234_567.86'>>>f"{Fraction(355,113):*>20.6e}"'********3.141593e+00'>>>old_price,new_price=499,672>>>"{:.2%} price increase".format(Fraction(new_price,old_price)-1)'34.67% price increase'